Effect of Hunting on Red Deer

Modelling Fecal Cortisol Metabolites

Nikolai German, Thomas Witzani, Ziqi Xu, Zhengchen Yuan, Baisu Zhou

Dr. Nicolas Ferry - Bavarian National Forest Park / Daniel Schlichting - StabLab

31 Jan 2025

Agenda

  1. The Background
  1. The Data
  1. The Models
  1. The Wrap-up

Motivation

  • Hunting activities might induce stress for red deer, even if non-lethal.
  • Goal: analyze how the distance in space and time to the (last) hunting event affects the stress in deer.

Data-Generating Process

  • A deer roams freely in the Bavarian Forest National Park.
  • Its movement is tracked by a GPS collar.
  • A hunting event happens.
  • After some time, the deer defecates. The defecation event.
  • Subsequently, Researchers go to the defecation location and collect a fecal sample.

FCMs as a Measure of Stress

  • Faecal Cortisol Metabolites (FCM) are substances found in feces of animals.
  • The FCM level is used to measure previous stress. Higher Stress \(\implies\) Higher FCM level.
  • Stress \(\Rightarrow\) secretion of certain hormones \(\Rightarrow\) gut retention \(\Rightarrow\) FCM.
  • Gut retention time \(\approx\) 19 hours.
  • Once defecated, FCM levels decay over time.

Huber et al (2003)

Approach

  • Model FCM levels - amongst other covariables - on spatial and temporal distance to hunting activities.

  • Expectations:

    • FCM levels higher when closer in time and space.
    • FCM levels lower, the more time passes between defecating and sampling.

Agenda

  1. The Background
  1. The Data
  1. The Models
  1. The Wrap-up

The Datasets

  • Movement Data
  • Hunting Events
  • FCM Data

Movement Data

  • Contains the location of the 40 collared deer
  • Period: Feb 2020 - Feb 2023
  • Movement is tracked in hourly intervals

Hunting Events

  • Contains location and date of hunting events
  • Observations: 720 events
  • 532 Observations with complete timestamp

FCM Data

Contains information of 809 faecal samples, including

  • the FCM level [ng/g],
  • the time and location of sampling,
  • to which deer the sample belongs,
  • when the defecation happened.

Distance Approximation

Deer location at the time of hunting event is approximated by linear interpolation.

Relevant Hunting Events

To identify relevant Hunting Events respective to a given FCM Sample, we introduce three selection parameters:

  • Gut retention time (GRT) target [hours]: Target Delay between Stress Event and Defecation
  • Gut retention time (GRT) thresholds [hours]: maximum temporal Distance between respective Deer and Hunting Event, with the Minimum beeing Zero
  • Distance threshold [km]: Maximum spatial Distance between respective Deer and potential Hunting Event

The Most Relevant Hunting Event

Among the relevant hunting events, the most relevant one is defined by one of the three introduced proximity criteria:

  • the closest in time to GRT = 19 hours (“closest in time”),
  • the closest in space (“nearest”), or
  • the one with the “highest score”.

Illustration

TimeDiff Distance 19 hours distance threshold GRT highthreshold Number of otherrelevant huntingevent = 3 Deer Hunting events Nearest Highestscore Closestin time(to 19 hours)

A hunting event is considered relevant to a FCM sample, if

  • the time difference between experiencing stress (hunting) and defecation is between the GRT thresholds, and
  • the distance between the deer and the hunting event is \(\leq\) distance threshold.

The Scoring Function

we define the Scoring function as following:

\[ S(d, t) \propto \begin{cases} \frac{1}{d^2} \cdot f_\textbf{t}(t), t \sim \mathcal{N}(\mu, \sigma^2) &|t \leq \mu \\ \frac{1}{d^2} \cdot f_\textbf{t}(t), t \sim \mathcal{Laplace}(\mu, b) &|t > \mu \end{cases} \] where: \[ \begin{align*} d & \text{: Distance } \\ t & \text{: Time Difference } \\ \mu & \text{: GRT target = 19 hours } \end{align*} \]

The Scoring Function

Scores relative to \(t\) and \(d\)

Effect of \(t\) on the Score

The Fused Data

Finish Datasets

We suggest three different Datasets for Modelling

DataSet GRT low GRT high Distance Threshold Proximity Criterion Deers Observations
1 0 36 10 last 35 149
2 0 36 10 nearest 35 147
3 0 200 15 score 36 207

Agenda

  1. The Background
  1. The Data
  1. The Models
  1. The Wrap-up

The Models

For Modelling, we consider the following covariates, defined for each pair of FCM sample and most relevant hunting event:

  • Time Difference
  • Distance
  • Sample Delay
  • Defecation Day (as Day of Year (1-366))
  • Number of other relevant hunting events

The Models

We chose two different approaches to Modelling:

  1. Machine Learning: a model, which minimizes the residuals, in our case a XGBoost Model
  2. Statistical Modelling: a model, which helps to understand the effects of our covariables, here a General Additive Mixed Model

A XGBoost

TBD

B Generalized Additive Mixed Model

  • Family: Gamma

  • Log link for interpretability.

  • Let \(i = 1,\dots,N\) be the indices of deer and \(j = 1,\dots,n_i\) be the indices of FCM measurements for each deer.

\[ \begin{eqnarray} \textup{FCM}_{ij} &\sim& \mathcal{Ga}\left( \nu, \frac{\nu}{\mu_{ij}} \right) \\ \mu_{ij} &=& \mathbb{E}(\textup{FCM}_{ij}) = \exp(\eta_{ij}) \\ \eta_{ij} &=& \beta_0 + \beta_1 \textup{Pregnant}_{ij} + \beta_2 \textup{NumberOtherHunts}_{ij} + \\ && f_1(\textup{TimeDiff}_{ij}) + f_2(\textup{Distance}_{ij}) + \\ && f_3(\textup{SampleDelay}_{ij}) + f_4(\textup{DefecationDay}_{ij}) + \\ && \gamma_{i}, \\ \gamma_i &\sim& \mathcal{N}(0, \sigma_\gamma^2). \end{eqnarray} \]

B Generalized Additive Mixed Model

Last

B Generalized Additive Mixed Model

Nearest

B Generalized Additive Mixed Model

Highest score

B Coefficient Table

Linear Effects:

Dataset Term Estimate Std. Error
Closest in Time (Intercept) 5.8243844 0.0533979
Closest in Time NumOtherHunts -0.1370438 0.0614158
Nearest (Intercept) 5.8123504 0.0541316
Nearest NumOtherHunts -0.1026115 0.0596574
Highest Score (Intercept) 5.8882327 0.0812529
Highest Score NumOtherHunts -0.0112701 0.0141569

Agenda

  1. The Background
  1. The Data
  1. The Models
  1. The Wrap-up

Conclusion

  • Not many observations after datafusion left for robust modelling

  • Trade-off between spatial and temporal distance

  • Sample Delay seems to be significant

  • Modelling Outcomes don’t show much difference

  • Trade-off between Complexity and Explainability

Discussion

  • How to minimize spatial and temporal distance at the same time?

  • How to use a bigger Part of the Data?

Effect of Hunting on Red Deer